Dynamic stochastic projection method for multistage stochastic variational inequalities

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-26 DOI:10.1007/s10589-024-00594-4

Bin Zhou, Jie Jiang, Hailin Sun

引用次数: 0

Abstract

Stochastic approximation (SA) type methods have been well studied for solving single-stage stochastic variational inequalities (SVIs). This paper proposes a dynamic stochastic projection method (DSPM) for solving multistage SVIs. In particular, we investigate an inexact single-stage SVI and present an inexact stochastic projection method (ISPM) for solving it. Then we give the DSPM to a three-stage SVI by applying the ISPM to each stage. We show that the DSPM can achieve an \(\mathcal {O}(\frac{1}{\epsilon ^2})\) convergence rate regarding to the total number of required scenarios for the three-stage SVI. We also extend the DSPM to the multistage SVI when the number of stages is larger than three. The numerical experiments illustrate the effectiveness and efficiency of the DSPM.

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多阶段随机变分不等式的动态随机投影法

对于求解单阶段随机变分不等式（SVI），随机逼近（SA）类型的方法已经得到了深入研究。本文提出了一种用于求解多阶段 SVI 的动态随机投影法 (DSPM)。我们特别研究了一个不精确的单阶段 SVI，并提出了一种用于求解该 SVI 的不精确随机投影法 (ISPM)。然后，我们通过对每个阶段应用 ISPM，将 DSPM 应用于三阶段 SVI。我们证明，对于三阶段 SVI 所需的场景总数，DSPM 可以达到 \(\mathcal {O}(\frac{1}{\epsilon ^2})\)收敛率。当阶段数大于三个时，我们还将 DSPM 扩展到多阶段 SVI。数值实验说明了 DSPM 的有效性和效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.